Covering functors without groups

Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation finite algebra by Riedtmann and later for finite dimensional algebras by Bongartz and Gabriel, R. Martinez-Villa and de la Pe\~na. The best understood class covering functors is that of Galois covering functors F: A -> B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Galois class and for which classical Galois covering-type results still hold. For instance, if F:A -> B is a balanced covering functor, where A and B are linear categories over an algebraically closed field, and B is tame, then A is tame.Comment: Some improvements have been made; in particular, the proof of Theorem 2 has been restructured and clarifie

The Intrinsic Fundamental Group of a Linear Category

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.Comment: Final version, to appear in Algebras and Representation Theor

The first Hochschild cohomology group of a schurian cluster-tilted algebra

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã.Fil: Assem, Ibrahim. University of Sherbrooke; CanadáFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Coverings of Laura Algebras: the Standard Case

In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components are standard), then this algebra has nice Galois coverings associated to the coverings of the connecting component. As a consequence, we show that the first Hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper Galois coverings.Comment: The main result on the non-standard case was reformulated due to an inaccuracy in the previous version. Lemma 6.1 was removed due to a simplification. The last section on the special biserial case was removed. Typos corrected and bibliography updated. Final version to appear in Journal of Algebr

Las ciudades del mañana: Gestión del suelo urbano en Colombia

América Latina no sólo se caracteriza porque la mayoría de su población reside en las ciudades, sino por el hecho de que en ellas anida la pobreza y abundan las áreas deterioradas y los asentamientos informales, con todo el daño que esto implica en materia de salud, educación y acceso a los servicios para sus habitantes. Sin embargo, esta realidad puede cambiarse. Así lo demuestra la experiencia de Colombia de los últimos 10 años, cuyas políticas pioneras se presentan en estas páginas. En Las ciudades del mañana se analizan instrumentos para la gestión y generación del suelo, esenciales para la transformación de las prácticas de planificación y gestión del desarrollo urbano. Asimismo, se resaltan casos exitosos de rehabilitación de áreas desmejoradas o abandonadas, y de construcción de vivienda social con altos estándares y atención al cuidado del medio ambiente en Bogotá y Medellín, y en el municipio de Pereira